Software package to research optimization problem for age structure of power plants basic types

The increase in the average age of the main equipment of the electric power system of Russia in recent decades, combined with inflation, leads to the need to develop strategies for reconstruction, modernization, and commissioning of new capacities. In this regard, the optimal control problem of the age structure of the power plants equipment is considered. The problem is set based on an integral model for the development of a large electric power system. The model takes into account the age structure of power plant equipment by identifying several age groups of equipment with different indices of their functioning. At the same time, the generating equipment is divided into several types according to the type of energy used. The mathematical model is a system of Volterra-type integral equations with variable lower and upper limits of integration, which describes the balance between the given level of electricity demand, the commissioning of new and decommissioning of obsolete equipment, as well as the shares of different types of power plants in the total composition of the electric power system. The optimality criterion is a functional reflecting cost of commissioning and operating the capacities. The specificity of the problem is the nonlinear occurrence of control parameters both in the objective functional and in the constraints. The existence and qualitative behavior of solutions to such problems require special analysis because no general theory exists. The paper presents a software package for solving the problem of optimal control of the age structure of the main equipment of power plants. The algorithm includes a numerical solution of the system of non-classical Volterra integral equations of the first kind using modified quadrature methods of right and middle rectangles. A method is proposed for taking into account constraints on the input capacities. Numerical calculations of the optimal development of the Unified Energy System of Russia until 2050 are carried out using real-life data. Using the developed software package, it is possible to solve the problem of optimal control of the age structure of power plant equipment for various variations of economic indicators.